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Figure 5.4 is a simple representation of the method applied to a linear regression problem; in this case, m = 2 observations, each providing a constraint on the y value, are suf cient for estimating the model parameters, which are the slope and intercept of the line. The hypothesis on the right is the one with the maximum number of inliers and the minimum LSE error. An example related to object tracking is also given by Fischler and Bolles [65] who t a three-dimensional model with a Euclidean pose to correspondences between known object points and noisy image measurements, under a calibrated perspective camera. This problem is also known as Perspective from n points (PnP), and can be solved in closed form if we have a minimum number m = 3 correspondences, each providing two constraints, known as the P3P problem. In fact, as shown in Fig. 5.5, three correspondences de ne a triangle in space, so that the solution can be obtained by estimating the distances a, b, c of the three vertices A, B, C from the camera center given the angles between image

The energy storage capability of ywheels can be improved by using the right material and increasing the moment of inertia, or spinning it at higher rotational velocities. Some designs use hollow cylinders for the rotor, which allows the mass to be concentrated at the outer radius of the ywheel and improves storage capability with a smaller weight increase in the storage system. Flywheel energy storage systems have capacities from 0.5 to 500 kWh. The ywheel itself loses less than 0.1% of the stored energy per hour if magnetic bearings are used. Two strategies have been used in the development of ywheels for power applications. One option is to increase the inertia by using a steel mass with a large radius and rotational velocities up to a few thousand revolutions per minute. A fairly standard motor and power electronic drive can be used as the power conversion interface for this type of ywheel. This design results in relatively large and heavy ywheel systems. The effective increase in run time for such systems rarely exceeds 1 second at rated load, which corresponds to a delivery of less than 5% of the additional stored energy in the wheel. Delivery of more energy would result in reduced rotational speed and hence reduced electrical frequency, which is usually unacceptable. Rotational energy losses also limit the long-term storage ability of this type of ywheel. To decouple the decrease in rotational speed from the stable electrical frequency needed by the grid, a system with variable speed controlled by a power electronic drive with recti cation and inversion electronics is usually implemented, as indicated in Figure 11.11. For such standard systems, the rotational speed is limited to approximately 10,000 rpm. Induction machines operating in eld-weakening mode can be employed.

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To summarize, the use of one-to-one backup requires installing new forwarding state at both the MP and the PLR. Because the backup protects a single main LSP, the amount of state that the MP, the PLR and all the nodes in the backup path must maintain increases proportionally to the number of LSPs protected. Using separate backup tunnels means that the depth of the label stack need not increase when traffic is forwarded from the main LSP to the backup.6 Furthermore, the fact that each backup services a single LSP allows tighter control over the backup tunnel and its properties. This is difficult with facility backup where multiple LSPs share the same backup. Regardless of the type of protection used, the time it takes to update the state in the forwarding engine following the failure detection adds to the total protection time. This is an important, though often overlooked, component in the total protection time. To achieve fast switchover, many implementations install the forwarding state for the protection path ahead of time. With the backup tunnel computed and signaled and the forwarding state in place to shift traffic from the main tunnel to the backup, let us now take a look at what happens after the failure of the protected link.

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